Astronomy & Astrophysics manuscript no. output c ESO 2019 October 28, 2019 Peculiar velocity cosmology with type Ia supernovae R. Graziani1, M. Rigault1, N. Regnault2, Ph. Gris1, A. Möller1, P. Antilogus2, P. Astier2, M. Betoule2, S. Bongard2, M. Briday3, J. Cohen-Tanugi4, Y. Copin3, H. M. Courtois3, D. Fouchez5, E. Gangler1, D. Guinet3, A. J. Hawken5, Y.-L. Kim3, P.-F. Léget2, J. Neveu6, Ph. Rosnet1 1 Université Clermont Auvergne, CNRS/IN2P3, Laboratoire de Physique de Clermont, F-63000 Clermont-Ferrand, France. e-mail: [email protected] 2 Laboratoire de Physique Nucléaire et des Hautes Energies, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, 4 place Jussieu, F-75005 Paris, France; Sorbonne Universités, UPMC Univ Paris 06, UMR 7585, LPNHE, F-75005, Paris, France. 3 Université de Lyon, Univ. Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, F-69622, Villeurbanne, France. 4 Université de Montpellier, CNRS/IN2P3, Laboratoire Univers et Particules de Montpellier. 5 Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France. 6 Laboratoire de l’Accélérateur Linéaire, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France. ABSTRACT Type Ia Supernovae have yet again the opportunity to revolutionize the field of cosmology as the new generation of surveys are acquiring thousands of nearby SNeIa opening a new era in cosmology: the direct measurement of the growth of structure parametrized by f D. This method is based on the SNeIa peculiar velocities derived from the residual to the Hubble law as direct tracers of the full gravitational potential caused by large scale structure. With this technique, we could probe not only the properties of dark energy, but also the laws of gravity. In this paper we present the analytical framework and forecasts. We show that ZTF and LSST will be able to reach 5% precision on f D by 2027. Our analysis is not significantly sensitive to photo-typing, but known selection functions and spectroscopic redshifts are mandatory. We finally introduce an idea of a dedicated spectrograph that would get all the required information in addition to boost the efficiency to each SNeIa so that we could reach the 5% precision within the first two years of LSST operation and the few percent level by the end of the survey. 1. Introduction to the standard model of cosmology. Interestingly, a first hint of physics beyond the standard model of cosmology has been seen Luminosity distances derived from observations of Type Ia Su- when comparing the sole other directly measurable cosmologi- pernovae (SNeIa) are a key tool to probe the expansion history of cal parameter: H0 [24, 25]). Predictions from the ΛCDM model the Universe. They are particularly powerful in the late Universe anchored on Planck (or WMAP) are indeed ∼ 5σ lower than (z < 0:3) where dark energy is the driving component. Within what is directly measured either by the direct distance ladder to- the next 5 years, first the Zwicky Transient Facility (ZTF) and ward SNeIa [25] or using time delays of strongly lensed quasar then the LSST will discover tens of thousands of nearby SNeIa images [30]. over a large fraction of the visible sky, thanks to large field of view and fast cadences. This opens a new avenue for SN Cos- Growth rate measurements based on peculiar velocities are mology: the direct measurement of the growth rate of structures currently relying on galaxy scaling relations like the Tully-Fisher in the recent Universe. (TFR) and Fundamental Plane (FP) relations. These distance in- Residuals to the Hubble law at low redshift are partially dicators lead to individual measurements 5 times less precise caused by the peculiar velocities of the SN host galaxies aris- than SNeIa, but, until now, have been easier to gather in a large ing by their interaction with the underlying gravitational poten- sample. The state-of-the-art 6dFGS [1] uses FP data to measure tial caused by large-scale structures in the universe. In practice, f D at the 15% precision level at redshift z = 0. Upcoming pecu- SN peculiar velocity leads to a difference between the observed liar velocity surveys such as TAIPAN ([4], FP) and WALLABY redshift and the redshift due to the cosmological expansion of ([13], TFR) are expected to achieve a 7% and 6.3% measurement the universe. As SN brightness can be used to determine the respectively, assuming no systematic error on the calibration of latter, the observed redshift can effectively be used to constrain their distance indicators. The growth rate can also be measured the line-of-sight peculiar velocity with respect to us. These mea- using Redshift Space Distortions (e.g with DESI, 10% measure- surements thus directly probe the total distribution of matter (in- ment at z ∼ 0:3) though in a redshift range where gravity models cluding dark matter) unlike measurements of galaxy distribution are hardly distinguishable. Moreover, this technique relies heav- only. The latter are sensitive to varying distributions for different ily on galaxy-bias models. We should also underline here that matter types ; the so called "galaxy-bias". SN Ia is unique to probe the universe at low redshift (z<0.2) The correlations of peculiar motions provide a direct mea- where dark energy is expected to dominate: weak lensing and surement of the growth rate of structure, f D, which depends on BAO, due to cosmic variance, are “blind” in this late universe. both the Hubble expansion law and the nature of gravity. The de- In this article we show that it is possible to achieve an un- pendence upon the gravity model (general relativity or modified precedentedly precise estimation of f D free from galaxy-bias γ gravity) can be parametrized using the growth index γ, f D = Ωm using SNeIa measurements. We present the derivation of the (e.g. Linder 2005). Any deviation from γ = 0:55 (corresponding growth rate of structure from SNeIa in section2 and we describe to a GR+ΛCDM model) would be an evidence for an extension the ZTF and LSST samples in section3. We will base our fore- Article number, page 1 of 6 A&A proofs: manuscript no. output cast on a realistic scenario for both of these surveys and we will samples have traditionally been used to derive such Redshift present our expectation in section4. More optimistic cases are Space Distortion (RSD) constraints on gravity. Constraints de- also shown to illustrate the impact of additional facilities such as rived from SN Ia samples will, however, be unique since the spectroscopic follow-up. Then in section5 we will discuss po- same field is responsible for both overdensity and velocity. When tential systematic effects in our analysis and the impact of miss- combined in a common analysis the sample variance limit is low- ing spectroscopy (SNeIa typing and host redshift) and a way to ered. solve these problems. We will conclude in section6. Different approaches exist to model the velocity-velocity and velocity-density correlations (e.g. Lavaux [14], Graziani et al. [7], Howlett [9]), and we adopt here a model-independant ap- 2. Type Ia supernovae as a probe of growth of proach by focusing on Fisher-Matrix estimations. The precision structure in measuring f D can be projected for different peculiar velocity surveys. The primary parameters that affect the precision are: On scales larger than individual galaxies, the peculiar motion v solid angle Ω, SN number density n, source intrinsic magni- of a SN at a position x is driven by the large scale mass distribu- tude dispersion σ , and for a distance-limited survey the maxi- tion surrounding the SN through the continuity equation: M mum distance rmax (alternatively redshift zmax). The dependence is most simply discerned in the Fisher information matrix r · v(x; a) = −aH(a) f (a)δ(x; a); (1) Z r Z k Z 1 " # Ω max max @C @C F r2k2 C−1 C−1 dµ dk dr i j = 2 Tr where a is the cosmological scale factor, H the Hubble parame- 8π r k −1 ∂λi ∂λ j d ln D min min ter, δ the density field and f ≡ d ln a is the linear growth rate. (2) These velocity measurements thus directly sample the full gravitational density field induced by the combined effects of where dark and baryonic matter, without any need for a galaxy-bias " 1 # Pδδ(k; µ, a) + n Pvδ(k; µ, a) correction. C(k; µ, a) = 2 ; (3) P k; µ, a P k; µ, a σ The peculiar velocities effectively induce correlated scatter vδ( ) vv( ) + n along the redshift axis of the SN Hubble diagram. At low red- and the peculiar-velocity uncertainty (σ) is related to mag- shifts probed by ZTF and LSST, and assuming magnitude scatter 2 nitude uncertainty σM and redshift uncertainty σz via σ = (e.g. due to intrinsic magnitude dispersion) is small, this effect is 2 2 ln(10) pronounced. (cσz) + 5 σM Haχ . The dependence of f D enters in the 2 velocity-velocity correlation Pvv / ( f Dµ) , the SN Ia host- 2 galaxy count overdensity power spectrum Pδδ / (bD) , and the 2.1. Peculiar velocities as a probe of gravity galaxy-velocity cross-correlation P / (bD) f Dµ. The uncer- vδ q −1 The statistical distribution of peculiar velocities can be directly tainty in the growth rate is bounded by σ f D = F . Equa- related to the natural laws that govern how primordial overden- f D; f D tion (2) is used in section4 to estimate forecasts for LSST and sities have evolved. The velocity-velocity power spectrum Pvv 2 ZTF. We discuss in subsection 5.1 the interest of adding the is sensitive to the growth of structure as Pvv / ( f Dµ) , where D is the spatially-independent “growth factor” in the linear evo- density-velocity correlation into the growth rate estimation.